Problem
A tri-diagonal matrix is a square matrix in which all entries are 0 except possibly those on the main diagonal and on the diagonals immediately above and below it. That is, T is a tri-diagonal matrix means that T (i, j)= 0 unless |i - j| ≤ 1.
(a) Devise a space-efficient storage scheme for tri-diagonal matrices, and give the corresponding index function.
(b) The transpose of a matrix is the matrix obtained by interchanging its rows with the corresponding columns. That is, matrix B is the transpose of matrix A means that B(j, i)= A(i, j) for all indices i and j corresponding to positions in the matrix. Design an algorithm that transposes a tri-diagonal matrix using the storage scheme devised in the previous part of the exercise.